Risk measurement and reporting (2) (Why risk reporting is important within…
Risk measurement and reporting (2)
Example correlations between risks
Inflation risk is heavily correlated with expense risk for most long-term financial products
Traditionally equity markets have moved in the opposite direction to interest rates (although this correlation has not been so obvious more recently).
Equity market falls are correlated with higher withdrawal rates on unit-linked savings products.
Operational risk is weakly correlated with all other risks, because if management are concentrating on dealing with these other areas they may not be concentrating on routine operational matters.
Longevity risk (e.g. immediate annuities) is strongly negatively correlated with mortality risk (e.g. term assurance).
A function which takes as inputs marginal cumulative distribution functions and outputs a joint cumulative distribution function.
It provides a way of calculating joint probabilities of risks, such as the probability of the return on the equity and bond portfolios both falling below certain levels
Different copulas are used to describe different degrees of dependence between random variables, including dependence in the tails of distributions.
Copulas are therefore useful for modelling tail risk, which enables organisations to assess capital requirements under extreme events (e.g. a 1 in 200-year event_
Measuring liability risks
Liability risks can be measured by an analysis of experience, e.g. actual deaths divided by expected death.
It is important to ensure consistent classification and measurement of the risk event and the exposure to risk.
Value at Risk
represents the maximum potential loss on a portfolio over a given future time period with a given degree of confidence. The loss may be expressed as an absolute amount or relative to some benchmark, e.g. the underperformance relative to an index.
Drawbacks of VaR
It is often calculated assuming a normal distribution of returns, whereas this is not necessarily true in practice as distributions may be 'fat-tailed' or skewed (e.g. portfolios exposed to credit risk, systematic bias, or derivatives exhibit non-normal distributions).
Var can be calculated using a different distribution but data is often sparse, particularly within the tails, and it is difficult to fit an accurate distribution.
VaR does not quantify the size of the tail, i.e. what the loss might be beyond the VaR confidence level
Tail VaR is the expected shortfall below a certain level, given that the shortfall has occurred.
e.g. if it is believed that the average loss on the worst 5% of possible outcomes for a portfolio is $5m, then the TVaR is $5m for the 5% tail.
A means of categorising the various risks to the company or individual
Against each risk the likely impact and probability of occurrence are recorded. The product of these measures gives an idea of the relative importance of the various risks.
The risk portfolio can be extended to indicate how each risk had been dealt with, e.g. retained (and the resulting capital requirements), diversified (and a revised assessment of the remaining combination of risks), mitigated through transfer (full or partial) or by other internal actions (and a revised assessment of the remaining risk).
For retained risks, the risk portfolio could also include details of control measures, reassessment after controls, risk owner, committee/ senior management with oversight, identification of concentrations of risk and the need for management action in these areas
Why risk reporting is important within a business (FRAUD CRIME)
Financing (appropriate price, reserves, capital requirements)
Rating agencies (to help determine appropriate rating)
Attractiveness to investors
Understand better (risks and their financial impact)
Determine appropriate control systems
Changes over time
Regulator (to provide greater understanding)
Monitor effectiveness of controls
Emerging risk identification
Why coherent risk reporting is important to enterprise risk management
As part of ERM, each business unit will have been given a risk exposure allocation. The benefits of diversification are likely to rely on each unit taking on the exposure allocated. Therefore, it is necessary that each unit report on the exposure they are taking, in a consistent way. If this does not happen, there is a risk that additional capital will be required to cover the undiversified risks.
A two-tier process for determining the capital to be held
A model is used to determine the risk event at the required level of probability, e.g. what size of fall in the equity market occurs with a 1 in 200 probability over one year? A stochastic model could be used to determine this.
A second model is used to determine the consequences/ cost of the risk event determined in 1. A deterministic model is likely to be used to determine this.
Issues to consider when assessing risk-based capital
Should the ruin probability be expressed over a single year or over the whole run-off the business?
Modelling more than two variables stochastically is probably impractical. Therefore, a method of assessing the correlation between variables is needed, e.g. correlation matrix
The effect of multiple risk events may be greater or less than the sum of individual risks due to interactions between risks
Some risks, such as operational risks, are highly subjective. In order to construct a plausible adverse scenario with a given ruin probability, it is necessary to look beyond risk evens that have already occurred.
Past data must be used with caution when estimating the consequences of rare events.